1. Field of the Invention
The present invention relates to a method of recognizing overlapped graphics in each degree of overlapping thereof on an image plane, which is applied to a CAD employed for designing the circuit pattern of an integrated circuit, a plotter for outputting graphics, and the like.
2. Description of the Prior Art
As is well known art, there have been proposed various methods of recognizing graphics in each degree of overlapping thereof on an image plane. For example, Japanese Patent Laying-Open Gazettes Nos. 57-14964/1982 and 59-60560/1984 disclosed such methods.
Japanese Patent Laying-Open Gazette No. 57-14964/1982 discloses a method of tracing a graphic in a prescribed direction from an end point thereof which is not included in a closed loop of another graphic, to switch to the closed loop of the other graphic upon reaching a crosspoint. In such a method, much time is required for steps of deciding whether a given point is in the interior or the exterior of the closed loop and sequentially tracing the loop. Further it is necessary to separately provide a step of recognizing AND graphics and OR graphics.
Japanese Patent Laying-Open Gazette No. 59-60560/1984 disclosed a method of dividing a plurality of given closed graphic at every slit, to recognize the degree of overlapping of the graphics. In such a method, segments forming the closed graphics are unnecessarily parted at the respective slits, and much time is required for changing the connecting relation among the segments in order to reproduce the recognized graphics
With respect to graphic including parametric portions which are represented by mathematical functions having parameters such as an arc designated by the radius thereof, the aforementioned processing is performed through replacement by linear segments in polygon approximation. However, much time is required for such polygon approximation, and the graphics are often recognized in incorrect forms.
According to the conventional methods, as hereinabove described, much time is required for overall processing due to the decision as to whether a given point is in the interior or the exterior of a closed loop, the processing of tracing the loop, the processing of unnecessarily dividing the segments in graphics and changing the connecting relation among the segments. Such tendency is increased as the graphics to be processed are complicated.
Further, additional steps must be carried out in order to output graphics in each degree of overlapping thereof.
In addition, there has been developed no method which can correctly perform arithmetic processing operation on graphics to output the same in each degree of overlapping in a short period with respect to graphics including parametric portions such as arcs.